Let's solve the equation:

$-22 + 4x = 7(x + 2) + 6x$

Step 1: Distribute on the right-hand side

Distribute the 7 across the parentheses:

$7(x + 2) = 7x + 14$

Now the equation becomes:

$-22 + 4x = 7x + 14 + 6x$

Step 2: Combine like terms on the right-hand side

Combine $7x$ and $6x$:

$-22 + 4x = 13x + 14$

Step 3: Move the variable terms to one side and constant terms to the other side

Subtract $4x$ from both sides:

$-22 = 9x + 14$

Now, subtract 14 from both sides:

$-22 - 14 = 9x$

$-36 = 9x$

Step 4: Solve for $x$

Divide both sides by 9:

$x = \frac{-36}{9} = -4$

So, the solution is:

$x = -4$

Would you like further explanation or have any questions about this process?

Here are some related questions:

1. How do you solve an equation with parentheses?
2. What are like terms in algebra, and how do you combine them?
3. How do you handle negative numbers in algebraic equations?
4. How do you check if a solution to an equation is correct?
5. What steps should be taken when solving for a variable in a multi-step equation?

Tip: Always double-check your work by substituting the value of $x$ back into the original equation to confirm it satisfies the equation.